Question 1

Which of the following best describes the relationship between sample size and statistical power in hypothesis testing?

Accepted Answer

Increasing sample size generally increases statistical power.

Question 2

In a study of cooperative hunting in lions, researchers found Cramer's V = 0.245 for the association between position and role. How should this effect size be interpreted?

Accepted Answer

It indicates a small effect size.

Question 3

Which of the following is a potential problem with using very large samples in statistical tests?

Accepted Answer

Very small effects may become statistically significant, even if they are not practically relevant.

Question 4

Given the formula for Cohen's d: $$d = \frac{m_1$ - m_2$}{s_{pooled}}$$, what does a value of $$d = 0.45$$ typically represent?

Accepted Answer

A small effect size.

Question 5

Which of the following is NOT affected by sample size, assuming all other factors are equal?

Accepted Answer

Cramer's V

Question 6

A researcher finds a statistically significant association ($$p \u003c 0.05) $$between two categorical variables, but Cramer's V is 0.085. What is the most appropriate interpretation?

Accepted Answer

There is a statistically significant effect, but it is too small to be practically relevant.

Question 7

Which formula is used to calculate the effect size for a two-sample t-test?

Accepted Answer

$$d = \frac{m_1$ - m_2$}{s_{pooled}}$$

Question 8

In the context of hypothesis testing, what does 'power' refer to?

Accepted Answer

The probability of correctly rejecting the null hypothesis when it is false.

Question 9

A study reports a statistically significant link between eating carrots and intelligence, but the improvement is only 0.00001 IQ points. What statistical concept does this scenario illustrate?

Accepted Answer

Statistical significance without practical relevance

Question 10

Which of the following is a general guideline for interpreting Cramer's V?

Accepted Answer

V  0.5: Large effect

Question 11

Which of the following scenarios is most likely to result in a lack of statistical power?

Accepted Answer

Small sample size and small effect

Question 12

If the p-value from a chi-square test is less than the significance level $$\alpha$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 13

Which of the following is NOT a recommended aspect to check when evaluating the meaningfulness of an effect?

Accepted Answer

Is the sample size larger than the population?

Question 14

Which formula is used to calculate Cramer's V for a chi-square test?

Accepted Answer

$$V = \sqrt{\frac{\$$chi^2$$}{n \cdot (min(r-1, c-1))}}$$

Question 15

In a study with uneven marginal distributions and rare categories, what is a potential issue with interpreting Cramer's V?

Accepted Answer

Cramer's V may underestimate the strength of association.

Question 16

Which of the following is the best definition of 'effect size' in the context of statistical analysis?

Accepted Answer

The magnitude of the difference or association, independent of sample size.

Question 17

A researcher conducts a census (complete survey of the population) and performs a statistical test. What is a potential issue with this approach?

Accepted Answer

Statistical inference is unnecessary because the population is already known.

Question 18

In the context of the 'rule of thumb' for odds ratios, which value would indicate a small effect?

Accepted Answer

$$OR \u003c 1.5$$

Question 19

A study on buttered toast finds the true proportion of toast landing butter-side down is 62%. If the sample size is 70, which value is closest to the power of the test to reject the null hypothesis?

Accepted Answer

0.75

Power, Sample Size, and Effect Size in Statistical Analysis

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